See my delicious list for satellite phone rentals:
http://www.delicious.com/philip/satphone

I haven't updated it this year, so some may have fallen by the wayside. Iridium is now working, but Globalstar has satellites that are being eaten alive by space radiation, and I recommend not using them.

Here's the key to renting a satphone: run the numbers on every company to see which is cheapest. The rates vary, shipping may or may not be included, phone rentals vary. You have to run the full numbers on each company to see which is cheapest. Some include free shipping but charge more per minute; some make you pay for shipping but charge lower fees for the phone. If you don't price the full costs for each company, you may pay more than you need to. They play with the prices to make it hard to compare.

My wife and I camp in Death Valley over Thanksgiving, and we always rent a satphone to take with us. It's cheap insurance against being stranded. One of our campmates used the phone to call AAA when his home-brewed electrical system on his RV fried and he couldn't start his engine. We've called to get the weather in Tahoe to see if we could get over Donner Pass.

Have spare batteries or a way to plug into an inverter for AC if you don't rent spare batteries. Some of our rentals have maintained their charge for a week, but some haven't. Test the phone before you leave - you don't want to be reading the manual to figure it out when you really, really need to make that call.